Midsummer is when Norway's oil capital is at its brightest. Near-continuous daylight illuminates this fascinating harbour city, with its mix of pretty wooden structures draped over the hills and along the quaysides, augmented by modern trappings. And as the oil business is not so slick in July, hotels offer bargains.

Touch down

Stavanger's Sola airport is served non-stop from Heathrow by BMI (0870 60 70 555; flybmi.com) and SAS (0870 60 727 727; flysas.co.uk); from Gatwick by Norwegian (020-8099 7254; norwegian.no); and from Aberdeen and Newcastle by SAS and its partner Wideroe in competition with Eastern Airways (08703 669100; easternairways.co.uk).

Airport buses (00 47 51 59 90 60; flybussen.no) leave the terminal every 20 minutes, covering the 14km to the centre in about 20 minutes and serving a number of points in the city, including the railway/bus station (1) and Fiskepirterminalen (2) ferry terminal. A one-way trip costs Nkr95 (£11); returns, valid a month, Nkr150 (£17.50).

Get your bearings

Stavanger is splendidly compact and attractive, and focused on the twin harbours of Vagen to the west and Ostre Havn to the east.

The oldest part is Gamle Stavanger, also known as Straen, rising west of Vagen and decorated by 173 wooden buildings. Today, the kernel of the city is the thumb of land extending between the harbours.

Inland from here, the buildings get younger – with the exception of the mighty cathedral (3), on the north shore of the city lake. The railway station (1) is on the south side.

Stavanger has an efficient bus service, with each stop in the city numbered, and traffic is never a problem; a network of tunnels keeps cars out of the centre.

The tourist office (4) is just above the cathedral at Domkirkeplassen 3 (00 47 51 85 92 00; regionstavanger.com). It opens 9am-8pm daily until the end of August. Besides maps and information, bikes are available to rent.

Check in

Room rates may be high, but so too is value – a breakfast buffet and free Wi-Fi are standard in Stavanger. Plumb on the quayside, the plum-coloured Victoria (5) at Skansegaten 1 (00 47 51 86 70 00; victoria-hotel.no) is the most atmospheric place to stay – a grand 19th-century creation that has been updated without losing its ambience. It is offering summer bargains: a standard double room in a fortnight's time costs as little as Nkr795 (£88).

Of Stavanger's many modern alternatives, the Thon Hotel Maritim (6) at Kongsgata 32 (00 47 51 85 0500; thonhotels.no) is probably the most appealing: a central and comfortable business hotel that, in July and at weekends, offers some deals starting at around Nkr1,902 (£221) including unlimited free coffee while lounging about in the stylish reception.

The lowest rates year-round can usually be found in the south of the city at Stavanger St Svithun (7) (00 47 51 51 26 00; hihostels.no), part of the national youth hostel network but unlike any hostel you may have stayed in. It is actually part of the university hospital complex, and is mostly occupied by the relatives of patients.

The nightly rate for a comfortable triple room is Nkr950 (£110), with a 10 per cent discount for YHA members.

Day one

Take a hike

Walk up to Valberg Tower (8) (00 47 90 72 63 94), built in 1850 as a watchtower intended to guard against fires in the city and aboard ships moored in the harbour. Even from the surrounds of the tower you get excellent views across the city; wait until 11am, when the tower opens, and for Nkr30 (£3.50) you get a splendid panorama from the top (to 3pm daily).

Window shopping

The main retail area spills prettily through the winding streets beneath Valberg Tower, with a concentration of boutiques on Ovre Holmegate. For large purchases, you can reclaim tax – Norway is outside the EU.

For British visitors feeling the financial pinch, Europe's most upmarket charity shop is Fretex (9) – the Salvation Army Store at the corner of Ovre Holmegate and Ostervag. And Tilbords (10), a friendly gift shop on Valberget, dispenses free coffee to passers-by.

Forty years ago this month, Norway's first oil field opened – and began the process of turning the nation into one of Europe's richest. The benefits – and costs – of this precious commodity are told in spectacular fashion at the Norwegian Petroleum Museum (12), which dominates the quayside at Havneringen (00 47 51 93 93 00; norskolje.museum.no). The chronicle begins with an official 1960s pronouncement that Norway will never have a viable oil industry, and does not shirk the dangers associated with exploitation of oil and gas; you can even test out an oil rig escape chute. In summer it opens 10am-7pm daily; admission is Nkr100 (£11.50).

As a 2008 European Capital of Culture, Stavanger is so serious about its heritage that it even has a museum devoted to promoting some of its other two-dozen museums. The MUST Infosenter (13) at Nedre Strandgate 21 ( museumstavanger.no) occupies a lovely former warehouse on the quayside; the upper floor has been transformed into a sailing museum explaining life on board a transatlantic sailing ship in 1899. Open 10am-5pm daily, admission free.

An aperitif

Boker og Borst (14) at Holmegata 32 (00 47 51 86 04 76; bokerogborst.com) is a colourful venue which does what its name suggests (it translates as "Books and Booze"). You can sip beer or cocktails while browsing through the shelves.

Dining with the locals

Timbuktu Sushi (15), by the waterside at Nedre Strandgate 15 (00 47 51 84 37 40; herlige-restauranter.no), sounds like the ultimate fusion restaurant. The sharing menus offer a taste of much of the menu – for Nkr490 (£57) you get to sample all the main courses – butterfish, halibut, duck and sirloin – plus all the starters or desserts.

Day two

Sunday morning:go to church

The Domkirken cathederal (3) dominates the city centre: a bulky, austere structure from the outside, but when it opens (for the 11am service on Sundays, erratically at other times) you discover a cavernous, atmospheric location that feels as though it is the work of giants. It is Norway's oldest church, with origins in the 12th century; the most striking sight is the baroque pulpit, resembling a ship's figurehead.

Take a hike

From the Domkirken (3), make a clockwise circuit of the lake, then go off at a tangent into Gamle Stavanger – the old part of the city that comprises a jumble of white clapboard structures set on cobbled lanes. Not all of these are cottages and shops: the Norwegian Canning Museum (16) at Ovre Strandgate 88 (00 47 51 84 27 00; stavanger.museum.no) occupies one of the dozens of former canning factories that dominated the city a century ago. It tells the messy but profitable story of sardine canning, and has a gallery of sardine-tin art: more compelling than it may sound. You can also try your hand at packing sardines.

Next, descend to Vagen, then walk around the magnificent harbour – which may well have one or two massive cruise ships in port. At the point where the Atlantic reaches deepest inland, watch out for one of Antony Gormley's bronze self-sculptures, planted here as part of a disjointed column stretching down from the Art Museum. Continue around the shore, following the "Blue Promenade" footpath to the Geopark – the bizarre concrete park outside the Norwegian Petroleum Museum (12), filled with redundant relics of the oil exploration business.

Out to brunch

Set on the ground floor of the Petroleum Museum (12), Bolgen & Moi (00 47 51 93 93 51; bolgenogmoi.no) is part of an upmarket chain, and ideally appreciated in the middle of the day, when its spectacular location shines at its best (11am-5pm daily). Seafood is the main strength, but you can opt for something simple such as soup or salad, served with panache.

Take a ride

Even under grey skies, it is worth taking the three-hour boat excursion from Stavanger to the spectacular Lysefjord. This is a journey that allows you to see the city from the sea, then to pass beneath one of the spectacular bridges created as a result of oil wealth, which marks the beginning of Lysefjord. The main focus for many passengers is Pulpit Rock, the wedge of rock 600m above the water. But the stories of settlements on the fjord are equally intriguing, and if the captain is game – and the water is flowing – you can get happily drenched as the ship almost dips beneath a spectacular waterfall.